What sets off the quarrel between Achilles and Agamemnon at the beginning of Homer’s The Iliad (ninth century B.C.)?

Agamemnon, commander-in-chief of the Greek armies at Troy, is forced to return a captive woman named Chryseis in order to stop a pestilence sent by the god Apollo at the beginning of Homer’s The Iliad.

Agamemnon demands Achilles’ captive Briseis in exchange. Achilles, in anger, refuses to fight for the Greeks any longer.